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Approximate Simulation Techniques and Distribution of an Extended Gamma Process

Author

Listed:
  • Zeina Al Masry

    (Université de Pau et des Pays de l’Adour)

  • Sophie Mercier

    (Université de Pau et des Pays de l’Adour)

  • Ghislain Verdier

    (Université de Pau et des Pays de l’Adour)

Abstract

In reliability theory, many papers use a standard Gamma process to model the evolution of the cumulative deterioration of a system over time. When the variance-to-mean ratio of the system deterioration level varies over time, the standard Gamma process is not convenient any more because it provides a constant ratio. A way to overcome this restriction is to consider the extended version of a Gamma process proposed by Cinlar (J Appl Probab 17:467–480, 1980). However, based on its technicality, the use of such a process for applicative purpose requires the preliminary development of technical tools for simulating its paths and for the numerical assessment of its distribution. This paper is devoted to these two points.

Suggested Citation

  • Zeina Al Masry & Sophie Mercier & Ghislain Verdier, 2017. "Approximate Simulation Techniques and Distribution of an Extended Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 213-235, March.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-015-9474-3
    DOI: 10.1007/s11009-015-9474-3
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    References listed on IDEAS

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    1. Guida, M. & Postiglione, F. & Pulcini, G., 2012. "A time-discrete extended gamma process for time-dependent degradation phenomena," Reliability Engineering and System Safety, Elsevier, vol. 105(C), pages 73-79.
    2. Ishwaran, Hemant & James, Lancelot F., 2004. "Computational Methods for Multiplicative Intensity Models Using Weighted Gamma Processes: Proportional Hazards, Marked Point Processes, and Panel Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 175-190, January.
    3. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
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    Cited by:

    1. Al Masry, Zeina & Rabehasaina, Landy & Verdier, Ghislain, 2022. "Change-level detection for Lévy subordinators," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 423-455.
    2. Sophie Mercier & Carmen Sangüesa, 2023. "A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 91-129, January.

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